Modlado y asegurameinto de flujo de fluidos pesados Modelado de crudo pesado:

desde la físico-química básica hasta el aseguramiento de flujo.

Sergio E. Quiñones-Cisneros (UNAM) Institutio de Investigaciones en Materiales – UNAM

Grupo SSC

(Resumen de avance proyecto Banco de Pruebas PEMEX - Dos Bocas)

Equipo Multidisciplinarlo de Teabajo Facultad de Ingeniería – UNAM

•  Teoría de fricción (antecedentes)

•  Modelado de fluidos Newtonianos

•  Modelo reológico para petróleo pesado

•  Aseguramiento de flujo

•  Conclusiones

Temario

NF kk µ=ar ppp +==σ

arf τττ +=

∑=

=1

,i

irirr pµτ ∑

==

1,

i

iaiaa pµτ

N

U F Fk u

uu δ+uu δ2+ hδ

hδhδ

τ

fτττ += 0

σ

σ

ff ηηητττ +=⇒+= 00

huδ

δτη =

Van der Waals: Amontons-Coulomb:

The Friction Theory

•  The general model depends on one scaling parameter:

η = η0 +η f

η f = ηc κ̂ apapc

⎛⎝⎜

⎞⎠⎟+ κ̂ r

prpc

⎛⎝⎜

⎞⎠⎟+ κ̂ rr

prpc

⎛⎝⎜

⎞⎠⎟

2⎡

⎣⎢⎢

⎤

⎦⎥⎥

�

ηc,i = KcMWi Pci

2 / 3

Tci1/ 6 (Uyehara & Watson, 1940)

The FT one-parameter model

ηc

n-Alkanes Results

hc (mP) SRK PR

C H4 152.930 3.98% 3.53%

C3 H8 249.734 1.41% 1.40%

n-C5 258.651 3.18% 2.81%

n-C8 256.174 1.54% 1.56%

n-C10 257.928 1.40% 1.36%

n-C15 229.852 1.44% 1.06%

n-C18 206.187 2.32% 1.91%

Overall 2.19% 2.02%

Vogel’s propane data

Original mixing rules

fηηη += 0 ( )⎥⎦

⎤⎢⎣

⎡= ∑

=

n

iiix

1,00 lnexp ηη

2rrrrraaf ppp κκκη ++=

∑∑∑===

===n

iirrirr

n

iiaia

n

iirir zzz

1,

1,

1, κκκκκκ

∑=

==n

i i

i

i

ii

MWxMM

MMMWxz

1εε 30.0=ε

Mixtures Results

AAD/%f -SRK f -PR f -PRSV

C1 + C3 2.28 2.06 2.37C1 + n-C4 3.38 2.88 2.55C1 + n-C6 4.43 4.07 4.27C1 + n-C10 7.6 6.94 6.37n-C5+n-C8 4 4.02 4.19n-C5+n-C10 3.8 3.7 3.69n-C6 + n-C7 1.91 2.11 1.78n-C7+n-C8 3.41 3.5 3.62n-C7+n-C9 1.66 2.09 2.14n-C8+n-C10 2.14 1.91 1.75n-C10+n-C16 4.84 5.26 3.94n-C5+n-C8+n-C10 3.85 3.74 3.76n-C10+n-C12+n-C14+n-C16 1.39 1.56 1.63

Modeling Newtonian oils

Pseudocomponents

�

ηc,i = KcMWi Pci

2 / 3

Tci1/ 6

(Uyehara & Watson, 1940)

To be tuned (Kc=7.95 n-alkanes)

η c [µP]N2 174.179CO2 376.872Methane 152.930Ethane 217.562Propane 249.734i-Butane 271.155n-Butane 257.682i-Pentane 275.073n-Pentane 258.651Hexane 257.841

Light Components Based on regular EOS

characterization

⇒η = ηL + KcηH

CS(n) Distribution

0

0.05

0.1

0.15

0.2

0

s

fdis

Heavy Fraction Characterization

Mass Distribution Function: Chi-Squared (CS)

∫−

=i

i

disi

s

sdsffm

1

∫−

=i

i

disi

i

s

sdsfs

fms

1

1ˆ

ii sMWMW ˆ=

Light Components (Excluded Mass)

The CS(n)

The CS(n)

The CS(n)

The CS(n)

Mass Characterization

Mass Characterization

Mass Characterization

Mass Characterization

Pc & Tc Scaling Equations

After n-alkanes

05

101520253035404550

0 200 400 600 800 1000 1200MW

Pc (b

ar)

020040060080010001200140016001800

Tc (K

)

Pc (Emp. Eqn.)Pc (KAP & EHS)Tc (Emp. Eqn.)Tc (KAP & EHS)

KAP & EHS: K. Aasberg-Petersen and E. H. Stenby

�

Tc = -423.587 +210.152 ln(MW )

�

Pc = fc exp 9.67283− 4.05288MW0.1( )

w Scaling Equation

After n-alkanes

0

0.5

1

1.5

2

2.5

10 100 1000MW

ω(Emp. Eqn.)

(KAP & EHS)

KAP & EHS: K. Aasberg-Petersen and E. H. Stenby

⎟⎠⎞⎜

⎝⎛= 0.1MW

15.1665-8.50471expω

Scaling Equations

�

Tc = -423.587 +210.152 ln(MW )

�

Pc = fc exp 9.67283− 4.05288MW0.1( )

⎟⎠⎞⎜

⎝⎛= 0.1MW

15.1665-8.50471expω

After n-alkanes

Tuned to match the saturation pressure.

(Only applies to the C7+ fractions)

05

101520253035404550

0 200 400 600 800 1000MW

Pc (b

ar)

n-AlkanesBasic EqnTuned Pc

HP/HT FT Viscosity Results

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 200 400 600 800 1000

Pressure (bar)

Vis

cosi

ty (

cP)

Viscosity Tuning: Based on data above

saturation

η = ηL + KcηH

Heavy Oil 1

T = 72.8°C

MW = 240.2 g/mol.

05

101520253035

0 50 100 150 200Pressure (bar)

Vis

cosi

ty (c

P)

Experimental

f-theory

T = 68.3°C

MW = 430.4 g/mol

0

200

400

600

800

1000

1200

0 50 100 150

Pressure (bar)

Vis

cosi

ty (

cP)

Experimental

f-theory

Heavy Oil 2

T = 35°C

MW = 316.6 g/mol

0500

10001500200025003000350040004500

0 50 100 150

Pressure (bar)

Vis

cosi

ty (c

P)

Experimentalf-theory

Heavy Oil 3

T = 47.8°C MW = 422.9 g/mol

0.95

0.96

0.97

0.98

0.99

1

0.0 50.0 100.0 150.0

Pressure (bars)

Den

sity

(g/c

c)

DataCalculated

1000

1500

2000

2500

3000

3500

0 50 100 150

Pressure (bar)

Vis

cosi

ty (c

P)

Experimental

f-theory

Heavy Oil 4

Blending

0

200

400

600

800

1000

1200

0.00% 1.00% 2.00% 3.00% 4.00% 5.00%Mass% NG

Vis

cosi

ty (m

Pa.

s)

Experimentalf-theory

Heavy Oil + NG

341.5 K

0

200

400

600

800

1000

1200

0 50 100 150 200 250Sat. Pressure (bar)

Vis

cosi

ty (c

P)

Experimentalf-theory

Heavy Oil + NG

Rheological model for crude oils

Linear FT model

η f = ηL + KcηH

Kc = K0 +

11+ γ 0 γ

0.7( ) exp 1+ s0 Tr − Ts( )( )6( ) s1 Tr − Ts( )( )3 + s2Tr − Ts( )0.5

⎡

⎣⎢⎢

⎤

⎦⎥⎥

s0 = 0.534555 K0 + 22.0187s1 = 0.045992 K0 −1.40495s2 = 2.51409 γ 0 +1.72677

(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)

Kc γ −>0⎯ →⎯⎯ K0 + ΔK

Rheological model for crude oils

Linear FT model

η f = ηL + KcηH

Kc = K0 +

11+ γ 0 γ

0.7( ) exp 1+ s0 Tr − Ts( )( )6( ) s1 Tr − Ts( )( )3 + s2Tr − Ts( )0.5

⎡

⎣⎢⎢

⎤

⎦⎥⎥

s0 = 0.534555 K0 + 22.0187s1 = 0.045992 K0 −1.40495s2 = 2.51409 γ 0 +1.72677

(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)

Rheological model for crude oils

Linear FT model

η f = ηL + KcηH

Kc = K0 +

11+ γ 0 γ

0.7( ) exp 1+ s0 Tr − Ts( )( )6( ) s1 Tr − Ts( )( )3 + s2Tr − Ts( )0.5

⎡

⎣⎢⎢

⎤

⎦⎥⎥

s0 = 0.534555 K0 + 22.0187s1 = 0.045992 K0 −1.40495s2 = 2.51409 γ 0 +1.72677

(Quiñones-Cisneros et al., Energy & Fuels 2008, 22, 799-804)

Kc γ −>∞⎯ →⎯⎯ K0

Rhelogical f-theory model results (Pedersen & Rønningsen, Energy & Fuels 2000, 14, 43–51)

2°C ≤ T ≤ 50°C

Oil 4

Phase Envelope (Oil 4 + 40% methane)

285 K 150 bar

110 bar

Oil 4

Dilution

Viscosity Thinning (Dilution: Oil 4 + 40% methane)

285 K 150 bar

110 bar

Oil 4

Shear thinning

Viscosity Thinning (Shear)

285 K 150 bar

110 bar

Oil 4

Shear thinning

Viscosity Thinning (Shear)

Propiedades fluidos mexicanos

•  Fluido Maya de referencia 21° API.

L1�Llegada

20�C

25�C

30�C

40�C

50�C60�C

1 2 5 10 20 50 100200 500

50

100

200

500

Γ� �s�1�

Η�mPa

s�

Propiedades fluidos mexicanos

•  Fluido Ku extra pesado (modelo corregido).

Fluid 12.2�API20�C

30�C

40�C

50�C60�C70�C80�C

113.5�C

0.01 0.1 1 10 100

100

200

500

1000

2000

50001� 1042� 104

Γ� �s�1�

Η�mPa

s�

Propiedades fluidos mexicanos

•  Predicción Fluido de 15° API.

Fluid 15�API20�C

30�C

40�C

50�C60�C70�C80�C

0.01 0.1 1 10 100

100

200

500

1000

2000

50001� 1042� 104

Γ� �s�1�

Η�mPa

s�

Propiedades fluidos mexicanos

•  Predicción Fluido de 17° API.

Fluid 17�API20�C

30�C

40�C

50�C60�C70�C80�C

0.01 0.1 1 10 100

100

200

500

1000

2000

5000

1� 104

Γ� �s�1�

Η�mPa

s�

Simulación Fluido 21° API 30° C L1�Llegada

20�C

25�C

30�C

40�C

50�C60�C

1 2 5 10 20 50 100200 500

50

100

200

500

Γ� �s�1�

Η�mPa

s�

Simulación Fluido 21° API 30° C L1�Llegada

20�C

25�C

30�C

40�C

50�C60�C

1 2 5 10 20 50 100200 500

50

100

200

500

Γ� �s�1�

Η�mPa

s�

Simulación Fluido 12.2° API 30° C

Simulación Fluido 12.2° API 20% mol CH4 30° C

Conclusiones

•  La correcta caracterización y modelado de los fluidos es fundamental.

•  La viscosidad de los fluidos puede ser adelgazada efectivamente medinate: –  Dilución

–  Mecánicamente.

•  Esto podría permitir un diseño novedoso y eficiente de lineas de transporte.

El desarrollo de un banco de pruebas para PEMEX es fundamental.

Conclusiones